Question

3. Sampling with and without replacement. Sarnpling urith replacement: A box contains tickets marked 1,2,...,u. A ticket is drawn at random from the box. Then this ticket is replaced in the box and a second ticket is drawn at random. Find the probabilities of the following events a) the first ticket drawn is number I and the second ticket is number 2 b) the numbers on the two tickets are consecutive integers, meaning the first numbir drawn is one less than the second number drawn e) the second number drawn is bigger than the first number drawn. Sampling uithout replaceeTt: d) Repeat a) through c) assuming instead that the first ticket drawn is not replaced, so the second ticket drawn must be different from the first.

question D good descriptive answer please.

Answer 1

Given that: the second number drawn is bigger than the first number drawn P (first number is less than second one) = P (first one is 1 and second one is n - 1 choices higher than this) + P (first one is 2 and second have n - 2 choices higher than this) + P (first one is 3 & second have n - 3 choices higher than this) + - - - - (1/n) * (n - 1)/n + (1/n) * (n - 2)/n + (1/n) * (n - 3)/n + (1/n) * (1/n) (1/n^2) * (1 + 2 + 3 + 4 + 5 + . . . . + (n - 1)) = (1/n^2) * ((n - 1)/2) * (1 + n - 1) = (n - 1) /(2 n) Without replacement: d) P (first number is 1 and second is 2) = (1/n) * (1/(n - 1)) \r\n = 1/(n (n - 1)) d - b) P (first number is one less than second one)